Speed of sound

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The speed of sound (c) can be written as:

c =  \sqrt{ \left. \frac{\partial p}{\partial \rho} \right\vert_S } = \sqrt{ \frac{B_S}{\rho} }

where B_S is the adiabatic bulk modulus, given by

B_S = \frac{C_p}{C_V} B_T

where C is the heat capacity and B_T is the isothermal bulk modulus, leading to

c =  \sqrt{  \frac{C_p B_T}{C_V \rho} }

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